Hampton pool is fantastic. It that was my local I might not do cold.
The usual advice is swim down so start going 2-3 times a week in the autumn. I'm not sure how to start, or in my case restart, in January.
Maybe get in the shallow end, splash water on chest/face, swim ~20m head up breast stroke then head in and maybe ~200m total. Repeat a 2-3 times over a week. Then start to build up the times. The main thing is don't feel like you have failed if you get out really quickly, just come back and have enough go quickly.
Also lay out your clothes for easy dressing afterwards, have 1 more layer than all of them to put put on and have a flask of hot drink or cafe available.